Simulation of Unilateral Constrained Systems with Many Bodies

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Modeling and analysis of rigid multibody systems with translational clearance joints based on the nonsmooth dynamics approach (2010, background): “Similarly, the measure for the so-called percussions corresponds to a Lagrangian multiplier which gathers both finite contact forces and impulsive contact forces ƒ, that is, dP D dt C ƒd [30].”
Application of the nonsmooth dynamics approach to model and analysis of the contact-impact events in cam-follower systems (2012, methodology): “Thus, this set of algebraic equations can be easily included in the Moreau time-stepping method, being the saddle point of the augmented Lagrangian found by employing, for instance, the modified Newton method, also called Newton–Raphson method [43, 54, 61].”
A comparative study of the viscoelastic constitutive models for frictionless contact interfaces in solids (2015, background): “Many researchers have considered the complementarity formulation associated with Moreau’s time-stepping algorithm for contact modeling in multibody systems over the last years [55-57].”